I have very good relative pitch and used to moonlight as a harpsichord tuner. I can tell you if an instrument is in equal temperament - an equal-tempered fifth

I have very good relative pitch and used to moonlight as a harpsichord tuner. I can tell you if an instrument is in equal temperament - an equal-tempered fifth and an equal-tempered third have very distinctive sounds. With enough time, I can also identify most of the common baroque temperaments: Just Intonation and quarter-comma meantone stick out like a sore thumb, but tunings like Werckmeister and the others that attempt to be close to equally tempered are harder to pick out by ear since you really need to hear a lot of the circle of fifths to identify which one is used. However, this skill isn't due to hearing a precise gap between the two notes, but listening to the beating of the overtones of the notes. It's a very different skill than what you learn in school to identify intervals. Also, professional string players can often tune equal tempered fifths (~2 cents flat of a pure fifth) precisely on their instruments.